Strange shadow over my mesh
It appears to me that the normals should be recomputed. In Edit Mode select all vertices with "A" and recalculate the normals by Ctrl-N. In addition, you may use "Smooth" from the toolbar in Object Mode to "smooth" the object. But that depends on how it should appear in general.
The vertices appear to be slightly "shifted", such that this kind of artifacts can happen. For me, it's completely ok to use the subdivide modifier. This modified subdivides all faces and reduces the angles of each of the faces.